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Chapter 5

ECO220Y1 Chapter 5 (5.1-5.6) Notes

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University of Toronto St. George
Jennifer Murdock

ECO220Y1 Textbook Notes Chapter 5: Displaying and Describing Quantitative Data (5.1 – 5.6) 5.1 Displaying Data Distributions  Histogram: can count the number of cases that fall into each bin, represent the counts as bars, and plot them against bin values. o Gaps are not in histograms unless gaps exist in the data. o Frequency – y-axis o Bin – x-axis o If we have n data points, we use about bins.  When a value falls right on a bin boundary, it can be put into either bin (left or right), but that process must be consistent with all other similar cases.  A relative frequency histogram’s vertical axis shows the percentage of the total count in each bin.  Stem-and-leaf display: similar to histograms but also give the individual values. o They use part of each number (called the stem) to name the bins. o To make the “leaves”, the next digit of the number is used.  I.e. the number 2.13 in stem-and-leaf looks like 2|3 o A -0 and a +0 must be used as stems since -0.3 is different from 0.3.  Quantitative Data Condition: that the data represent values of a quantitative variable. 5.2 Shape  Three things to pay attention to when describing distribution: o Shape o Centre o Mode  The shape of a distribution is described in terms of its mode(s), its symmetry, and whether it has any gaps or outlying values.  Mode: defined as the single value that appears most often (categorical variables). o Also defined as the peak in a histogram (quantitative variables).  Unimodal: a distribution whose histogram has one main hump.  Bimodal: a distribution whose histogram has two main humps.  Multimodal: a distribution whose histogram has three of more main humps.  Approximately uniform distribution: a distribution that doesn’t appear to have any clear mode.  Approximately symmetric distribution: when a distribution can be divided into two parts that look (approximately) like mirror images.  Tails: the (usually) thinner ends of a distribution.  Skewed distribution: when one tail stretches out farther than the other (skewed to the side of the longer tail).  Outliers (stragglers): points that stand off away from the body of the data distribution. o I.e. studying personal wealth with Bill Gates in your sample (Bill Gates’ point would be an outlier). o Can provide exciting/interesting information about the data.  Looking at a histogram at several different bin widths can help you see how persistent some of the features are. 5.3 Centre  When a histogram is unimodal and symmetric, most people would point to the centre of the distribution to describe a typical price change.  A bar over any symbol indicates the mean of that quantity. ̅  means “sum”.  Mean of y: the sum of all the values of variable y divided by the number of data values.  Median: the value that splits a histogram into two equal areas. o A better description of a distribution then the mean. The mean may be represented by the Which doesn’t describe the data as well as the me
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